FLOW-3D consumer products

Free surface flows are common in the design and manufacture of consumer products used in both the home and office environment. Bottle filling is, for instance, a process which takes place on a large scale every day. Designing such a process to minimize waste while maximizing production speed can lead to significant cost savings over time. FLOW-3D can also be used to design spray nozzles, model absorptive capabilities of porous materials and other consumer goods components. FLOW-3D‘s advanced multiphysics models including air entrainment, porous media, and surface tension make it easy to accurately simulate and optimize consumer product designs.


Entrained air can bulk up the volume of liquid as a container is being filled on a production line. The image on the left below shows 1.2 seconds of filling a bottle that is approximately 20 cm in height. The color shading indicates the volume fraction of air in the liquid. Because of the short time and high degree of mixing in the bottle the air has not had time to rise to the surface and escape. However, as the image on the right shows, after an additional period of about 1.7 seconds, the reduction in liquid volume resulting from air rising to the surface is clearly visible. FLOW-3D‘s drift flux model allows the separation of components such as air bubbles in liquid to separate out.

In by 9, out by 5

This article, describing how FLOW-3D was used to model the filling of a new Tide bottle design, was contributed by John McKibben – Technical Section Head, The Procter and Gamble Company.

Imagine it is 9:00 in the morning and you get an urgent e-mail.

 We just realized that one of our new Tide® bottle designs fills onto the handle and may have an issue on our filling equipment. We don’t have any prototype bottles – and won’t for several weeks. The designers and consumers love the look of the design, but the way it fills could be a show stopper for our production facilities.

When I was presented with this situation, I started responding by asking for a stereo-lithography (.stl) file of the 3D geometry (Figure 1) and I would see what I could do. I knew that FLOW-3D could use the .stl file to input the geometry and should be able to solve the free-surface problem for the filling. I expected this to give good qualitative understanding of the potential issues, but was a little uncertain about how accurate it would be for this application.

bottle geometry

Setting up and Running the Simulation

About 1:00 in the afternoon, I received the geometry files, flowrates, and fluid properties. Within a few hours the simulation was up and running, delivering preliminary results. I invited my customer over to take a quick look at the results and he brought along his “boss’s boss” to take a look too. So, by 5:00 in the evening, we were looking at the preliminary results and determined that the original concern wasn’t an issue.

The results did pose a few other questions however. Filling onto the handle created a lot of breakup of the incoming fluid jet. I knew this would increase the amount of entrained air and foam (we are filling laundry detergent after all). I decided to test the FLOW-3D air entrainment model. This model had been originally developed for turbulent jets, and I was uncertain how well it would perform when looking at this laminar flow problem.

Bottle filling simulation
Figure 2: Filled results
Bottle filling simulation and validation
Figure 3: Experimental comparison

Figure 2 shows results of the bottle filling model with and without the air entrainment model. Notice that there is a significant increase in the fill level when the entrained air is included. Notice that the entrained air doesn’t force fluid out of the top of the bottle, but it is close enough that we need to confirm the air entrainment accuracy. Figure 3 compares the air entrained level with images from an experiment run several weeks later (once prototype bottles were available). The qualitative agreement of the jet breakup and fill levels are excellent and provided confirmation that the simulation was sufficiently accurate to screen bottle designs.


Ever wonder how toilets work? They’re actually quite complicated. When the handle is pushed, water begins to fill the bowl. When the fluid level in the bowl rises above the top of the trap (behind the bowl), a weir-type flow begins. When the flow is fast enough, a bubble forms in the top of the trap creating a siphon. At that point, the siphon pulls the water out of the bowl and the toilet flushes. In many locales, water conservation is an important issue, and low-flow toilets are required for both home and commercial use. But if a toilet doesn’t get the job done on the first try, the water-conservative objective is defeated. FLOW-3D can be used to model various designs to achieve the optimum results.

Food Processing

The food processing industry has diverse requirements for managing complex fluids, typically non-Newtonian fluids, slurry, mixtures of solids and fluids, to optimally design and manufacture dispensing equipment. This is essential for consistency and durability of commercial grade equipment and their quality. Also, innovation of packaging designs can clearly distinguish one product apart from another. For instance, dispensing honey, ketchup or creamer cleanly and precisely may be a choice a consumer makes at the store. Transporting and storage requirements call for better engineering of shapes and more choices of container materials. Fluid loads during motion or dropping of a 1.5 liter bottle of water or laundry detergent can be an important part of design upstream.

Viscous fluids such as honey, corn syrup, and toothpaste commonly exhibit a tendency to form coils when they contact a solid surface. While this effect is interesting and fun to observe, it maybe unwelcome in packaging processes where it can cause air to be entrained into the product and make packaging difficult. The conditions under which coiling occurs depends on the viscosity of the fluid, the distance through which the fluid falls, and the velocity of the fluid. FLOW-3D provides an accurate tool for studying the various physical process parameters to help design an efficient process.


Over the past few decades, there has been much progress in understanding mixing mostly due to advances in computerized measurement and simulation techniques. Thanks to ongoing advances in flow modeling technology, detailed insight of the flow-dependent processes in mixing equipment can easily be simulated and understood using CFD software. Today, a wide range of applications from blending to solid suspension, from heat transfer in jacketed reactors to fermentation are modeled using FLOW-3D‘s mixing technology. FLOW-3D simulations can help evaluate key mixing parameters, such as blending time, circulation, and power number in any configuration of impellers and mixing conditions for any vessel geometry. These simulations complement using experimental methods. The use of CFD software to predict and understand the flow-dependent processes in such equipment can enhance product quality and reduce both cost and time to market of many products.

Non-Newtonian Fluids

Non-Newtonian fluids such as blood, ketchup, toothpaste, shampoo, paint and lotion have complex rheology with varying viscosities. FLOW-3D models such fluids with non-Newtonian viscosities that are strain and/or temperature dependent. Shear and temperature dependent viscosities are described with either Carreau, the power law functions or simply through a tabular input. Time-dependent or thixotropic behavior, characteristic of some polymers, ceramic and semi-solid metals, can also be simulated.

Hand lotion pumps are often associated with several design issues. It is important for the pump to work effectively without trapping air voids and generate a continuous stream of lotion. A good design requires less effort and would ideally direct the lotion to a desired place. FLOW-3D‘s Moving Object model is used to simulate the nozzle being pushed down, thereby pressurizing the lotion in the reservoir. The pressure in the lotion and the force required to extract lotion can be studied. Several design variables can easily analyzed within the same stationary structured mesh.

Porous Materials

Numerical modeling of the transport of fluid in porous media can be a challenge, but FLOW-3D includes many valuable features for the solution of problems involving porous materials. The FAVOR™ technique contains necessary porosity variables to enable the user to represent a continuous porous media. FLOW-3D allows users to simulate both saturated and unsaturated flow conditions. A power law relation allows users to model the non-linear relationship between capillary pressure and saturation in the unsaturated flow conditions. Separate filling and draining curves can be used to model the phenomenon of hysteresis. Different porosity, permeability and wettability properties can be assigned to different obstacles, even when in direct contact with one another. Permeability can be specified based on flow direction, enabling the user to model anisotropic behavior of porous media. Heat transfer between fluid and the porous media may be taken into account.


Swirl-spray nozzles are a common way to dispense liquids in chemical cleaners, medicines and fuels. For successful atomization of the liquid, it is usually necessary to form an air core that penetrates into the nozzle. CFD is an effective way to explore the influence of geometry, swirl velocity, and fluid properties for an optimum spray cone.

In this example, a two-dimensional axisymmetric swirl flow has been simulated. An air core along the axis of symmetry has nearly penetrated up the entire length of the nozzle. The left plot is a pressure distribution with the vectors representing a velocity distribution in the plane. The right plot is colored by the swirl component of velocity with red indicating the higher values.

It is not possible to directly compute the complete atomizations of a spray because the scales of the spray cone and droplet sizes are too broad. Also, atomization is a chaotic process closely tied to external perturbations, microscopic imperfections in a nozzle and other influences. However, being able to predict the properties of a spray cone as it leaves the nozzle (i.e., wall thickness, cone angle, axial and azimuthal velocities) goes a long way toward optimizing this type of flow device.

Swirl spray nozzles
FLOW-3D simulation of a swirl spray nozzle

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